#(Sin theta - cos theta +1)/(sin theta+ cos theta -1) =1 / (sec theta - tan theta)#?

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dk_ch Share
Oct 12, 2017

#LHS=(Sin theta - cos theta +1)/(sin theta+ cos theta -1)#

#=(costheta(sintheta - cos theta +1))/(costheta(sin theta+ cos theta -1))#

#=(costheta(sintheta - cos theta +1))/(costhetasin theta+ cos^2 theta -costheta)#

#=(costheta(sintheta - cos theta +1))/(costhetasin theta-costheta+1- sin^2 theta )#

#=(costheta(sintheta - cos theta +1))/(1- sin^2 theta -costheta+sinthetacostheta)#

#=(costheta(sintheta - cos theta +1))/((1- sin theta )(1+sintheta)-costheta(1-sintheta)#

#=(costheta(sintheta - cos theta +1))/((1- sin theta )(1+sintheta-costheta)#

#=costheta/(1- sin theta )#

#=(costheta/costheta)/((1- sin theta )/costheta)#

#=1/(1/costheta- sin theta /costheta)#

# =1 / (sec theta - tan theta)=RHS#

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